Exact analytical solutions in some areas of solid mechanics, in particular problems in the theory of plates, have long been regarded as bottlenecks in the development of elasticity. In contrast to the traditional solution methodologies, such as Timoshenko’s approach in the theory of elasticity for which the main technique is the semi-inverse method, this book presents a new approach based on the Hamiltonian principle and the symplectic duality system where solutions are derived in a rational manner in the symplectic space. Dissimilar to the conventional Euclidean space with one kind of variables, the symplectic space with dual variables thus provides a fundamental breakthrough. A unique feature of this symplectic approach is the classical bending problems in solid mechanics now become eigenvalue problems and the symplectic bending deflection solutions are constituted by expansion of eigenvectors. The classical solutions are subsets of the more general symplectic solutions.This book explains the new solution methodology by discussing plane isotropic elasticity, multiple layered plate, anisotropic elasticity, sectorial plate and thin plate bending problems in detail. A number of existing problems without analytical solutions within the framework of classical approaches are solved analytically using this symplectic approach. Symplectic methodologies can be applied not only to problems in elasticity, but also to other solid mechanics problems. In addition, it can also be extended to various engineering mechanics and mathematical physics fields, such as vibration, wave propagation, control theory, electromagnetism and quantum mechanics.
Ngôn ngữ Anh ● định dạng PDF ● Trang 316 ● ISBN 9789812778727 ● Kích thước tập tin 3.6 MB ● Nhà xuất bản World Scientific Publishing Company ● Thành phố Singapore ● Quốc gia SG ● Được phát hành 2009 ● Có thể tải xuống 24 tháng ● Tiền tệ EUR ● TÔI 2446367 ● Sao chép bảo vệ Adobe DRM
Yêu cầu trình đọc ebook có khả năng DRM